David Pollard of Pennsylvania State University, and Robert DeConto of the University of Massachusetts used a computer model to simulate the behaviour of the ice sheet over the past five million years.

They focused on a period called the Pliocene, some five to three million years ago, when temperatures were similar to those expected in the coming centuries. The scientists found that the West Antarctic ice sheet melted and reformed several times. Each switch took just a few thousand years.

The results are bolstered by a separate analysis of sediment dug from underneath the Antarctic Ross ice shelf, which also indicate periodic large-scale melting during that period. Both studies are published tomorrow in the journal Nature.

Pollard said: "The modelling shows it [the ice sheet collapse] has happened with regularity in the past and will happen again, driven by ocean warming."

He said more studies were needed to work out what level of ocean warming in the region would provoke another collapse. The 5C figure in the new paper is a "rough number" he said. "It could be 3C or it could be 6C."

Warmer oceans would melt the floating ice sheets around Antarctica, which currently block the sea's access to larger, ground-based ice sheets further towards the continent's interior. With the floating ice sheets gone, the land-based ice would be free to melt and so raise sea levels.

Glaciologists call such an event a collapse, but Pollard said it would not be rapid, and would take thousands of years to unfold: "We had a bit of a debate whether to use the word collapse in the paper. It's not something like an avalanche."

How quickly the West Antarctic and Greenland ice sheets could break up and melt has become a hot topic in climate science. The 2007 report from the Intergovernmental Panel on Climate Change said not enough was known to make any predictions. Since then some scientists have warned that the ice sheets are more unstable than realised – and that sea levels could rise faster than expected.